Ah yes... this one has been around a few boards lately... I was like you guys, until I too was turned. At first glance it seems easy- but once you figure it out and are convinced of the physics, you slap your head.
Here's a "pro's" article on the subject:
The Pilot's Lounge #94: It's The Medium, Manfred
There's a new aviation myth running around the Internet. It involves a conveyer-belt runway and misuse of aerodynamics and ... well, it's better if AVweb's Rick Durden explains it all himself in The Pilot's Lounge.
By Rick Durden
Columnist
The Pilot's Lounge
I heard the commotion as I started down the hall from the flight school to the Pilot's Lounge at the virtual airport. In the few moments it took to get to the door of the Lounge, individual voices became clear, split into two very vocal camps: The vehement "Yes it will!" calls being answered by an equally intense "No it won't!" I thought back to some of the stronger disagreements that had been aired here, such as the use of flaps on landing, but this one seemed a little louder and I wondered whether Old Hack and some of the bigger guys might have to separate combatants.
I stood off to the side and tried to get a handle on the conflict. Old Hack saw me and sidled over with a silly grin on his face. "These guys spend way too much time on the Internet," he said. "Someone has just come up with what looks like a 21st-century version of the old "downwind turn" foolishness and now the engineers and the soft-science folks are having at it."
The "Fatal" Downwind Turn
For those who don't recall the "downwind turn" tale of the last century, it goes like this: People observed that pilots who were flying relatively low on a heading that took them into the wind had a surprisingly high rate of impact with the ground or obstructions if they rolled into a turn and proceeded to a heading that was with the wind direction, or downwind. There were those who insisted that the airplane could not accelerate fast enough in the turn to make the necessary groundspeed change so as to stay above stall speed and thus they crashed.
As an example, we'll take a pilot with a reputation for good stick and rudder skills, a certain Manfred. We'll magically reincarnate him from the Western Front of World War I (where he had perished) and put him in a 65-hp, Piper J-3 Cub. Its cruise speed is pretty close to the Fokker Dr-I that Manfred last flew -- call it 80 mph. (The Fokker Triplane was so maneuverable few enemy pilots ever figured out it was astonishingly slow.)
We'll point Manfred and the J-3 northbound at 500 feet AGL into the teeth of a 40-mph headwind. His groundspeed is, therefore, 40 mph. Now we'll have him roll into a turn and change directions 180 degrees until he is headed south, directly downwind. We'll have him make the turn in 30 seconds, a twice-standard-rate turn. At that airspeed, it's not very steep and certainly not at all unsafe. The next consideration is that in those 30 seconds, Manfred's J-3 has to accelerate from a groundspeed of 40 mph to a groundspeed of 120 mph in order to still be moving through the air at 80 mph. In fact, if he does not accelerate through that needed 80 mph change in groundspeed, the airplane could stall because the airspeed would have dropped off radically.
There were those who were convinced that it was impossible for a 65 hp J-3 to increase its groundspeed by 80 mph in 30 seconds, and therefore the airplane would stall, which was what made downwind turns so dangerous.
Fortunately, back when this was being debated, rationality prevailed. It was pointed out that the airplane was flying through the air, its propeller was acting upon the air and its wings were moving in an airmass. Thus, when it made its turn, its airspeed didn't change. The airplane continued to move through the air at 80 mph. Its groundspeed changed solely because of the fact that the mass of air in which it was operating, the medium upon which it was acting, was moving.
Had the air been calm, Manfred and his J-3 would have had a groundspeed that matched his airspeed.
Interestingly enough, when the famous aviator, Jimmy Doolittle was sent by the Army to M.I.T. to study in the mid-1920s, his dissertation for his Ph.D. included some of this discussion, so the problem's been solved for some time; it just took most of the rest of the century for the understanding to trickle down. (Yeah, that air-racing, aerobatic, military pilot also had one of the first Ph.D.s awarded in aeronautical engineering.) Doolittle also hypothesized that the frequency of crashes during such turns was the visual effect of the rapidly increasing groundspeed causing pilots to believe that the airplane was suddenly going very fast and pulling back on the stick or throttle, leading to a stall or descent into the ground.
For those who still didn't understand that the downwind turn had no effect on the airplane, all it took was a flight on a day with some wind above a solid deck of clouds. Making a few circles made it clear that the airplane and its pilot could not tell anything about the direction of the wind while turning.
Conveyer-Belt Runway
What I learned from Old Hack was that an updated version of a question aimed at confusing folks over relative measurements of airplane motion and the medium in which it operates had shown up on the Internet, and it was causing the fracas in the Lounge.
The question that has been going around is not particularly artfully worded, and I think that has caused some of the disagreements, but I'll repeat it as it is shown: "On a day with absolutely calm wind, a plane is standing on a runway that can move (some sort of band conveyor). The plane moves in one direction, while the conveyor moves in the opposite direction. The conveyor has a control system that tracks the plane speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction). Can the airplane ever take off?"
My comment: Notice that the question does not state that the conveyor's movement keeps the airplane over the starting position relative to the ground, just that it moves in the direction opposite to any movement of the airplane.
Initially, about a third of the folks here said that the airplane could not ever takeoff, because the conveyor would overcome the speed of the airplane and it could never get any airspeed. The rest said the airplane would fly.
The "It won't fly, Rocky" group said that the conveyor would hold back the airplane. They asked us to imagine a person running on a treadmill. As he or she sped up, the treadmill would be programmed to speed up, just as the conveyor in the problem, and the person would remain over the same locus on the earth, while running as fast as possible.
The argument was that if the airplane started to move forward, the conveyor program was set up to move the conveyor at exactly that speed, in the opposite direction, thus, the airplane would never move relative to the ground, and, because the air was calm, it could never get any wind over its wings. One of the analogies presented was the person rowing at three mph upstream in a river on a calm day. However, the current was flowing downstream at three mph, so the resultant speed with reference to the stream bank and air was zero, and thus there was no wind on the rowboat.
I watched and listened to the disagreement for a while and was fascinated to see that the argument seemed to split between those who had some engineering or math background, all of whom said the airplane would takeoff and fly without any problem; and those with some other background, who visualized the airplane as having to push against the conveyor in order to gain speed. Because the conveyor equaled the airplane's push against the conveyor, the airplane stayed in one place over the ground and in the calm air could not get any airspeed and fly.
It was an interesting argument, but as things progressed, more rational heads prevailed, pointing out that the airplanes do not apply their thrust via their wheels, so the conveyor belt is irrelevant to whether the airplane will takeoff. One guy even got one of those rubber band powered wood and plastic airplane that sell for about a buck, put it on the treadmill someone foolishly donated to the Lounge years ago, thinking that pilots might actually exercise. He wound up the rubber band, set the treadmill to be level, and at its highest speed. Then he simultaneously set the airplane on the treadmill and let the prop start to turn. It took off without moving the slightest bit backwards.
Manfred In The 21st Century
OK, let's figure out why the airplane will fly.
We'll use Manfred again. Although we're bringing him forward into the 21st Century, we'll still let him use the 65 hp J-3. It doesn't really matter what airplane he flies, but he got used to the J-3 while he was demonstrating downwind turns and this one happens to have lifting rings on the top of the fuselage. It's also been modified with a starter so no one has to swing the prop.
Manfred's in the airplane. Old Hack has the Army-surplus crane fired up and he's picking up the J-3 and Manfred and carrying them over to Runway 27, which has been transformed into a 3,000-foot conveyor belt. It is a calm day. The conveyor drive is programmed so that if Manfred can start to move in the J-3, if he can generate any airspeed or groundspeed, the conveyor will move toward the east (remember Manfred and the J-3 are facing west) at exactly the speed of the air/groundspeed. Because the wind is calm, if Manfred can generate any indicated airspeed, he will also be generating precisely the same groundspeed. Groundspeed, of course being relative to the ground of the airport surrounding the conveyor belt runway. So, the speed of the conveyor belt eastbound will be the same as Manfred's indicated airspeed, westbound.
(con't)